Energy-efficient regeneration routing in satellite optical networks under translucent optical payload architectures

Yu Liu; Xin Li; Daixuan Li; Shanguo Huang

doi:10.1364/OE.519468

1. Introduction

Due to the high cost and difficulties of fiber facility construction, the terrestrial optical network (TON) cannot provide comprehensive communication coverage for any remote areas [1]. Low-earth-orbit (LEO) satellite network is an important part for the next-generation network to provide the comprehensive-coverage and low-latency communication services for worldwide users [2]. Free-space optical (FSO) communication is receiving high attention as an attractive alternative to radio frequency (RF) communication for satellite interconnection, holding the advantages of wide available bandwidth, immunity to interference, and small terminal size [3]. Different countries have carried out numerous researches on inter-satellite optical communication. The European data relay system using laser inter-satellite links (LISLs) has been applied in commercial applications [4–6]. In [7], the performance of the LISL with the data rate of 40 Gbps was measured. Mynaric’s laser terminal for LEO satellites is promising to provide the LISL with the data rate of 10 Gbps over distances of up to 4500 km [8]. Leading companies, such as SpaceX and Telesat, are employing LISLs for the interconnection between LEO satellites to form the satellite optical network (SON) to provide low-delay and large-bandwidth communication services [9].

Because of the relative movement between the LEO satellite and the earth, LEO satellites cannot use solar panels to power normal operation when the earth blocks sunlight (being in eclipse), and the rechargeable battery is an important component to provide the energy supply for satellites in eclipse [10]. The depth of discharge (DOD) directly affects battery life [11], and unrestrained use of batteries at a deep DOD will accelerate battery aging, shortening satellite’s lifetime seriously [12]. Considering the expensive cost of satellite construction and launch, alleviating battery aging and prolonging satellite lifetime are important for SONs. Many energy-efficient routing schemes have been proposed to reduce battery life consumption [13–16], but they don’t consider SON’s feature that lightpaths can pass through on-board payloads transparently (lightpath bypass), and cannot fully exploit the advantage of the SON in terms of energy efficiency.

Currently, the wavelength division multiplexing (WDM) technology is being applied in SONs [17], which can not only make efficient use of optical bandwidth but also minimize on-board processing, reducing the energy consumption of satellites. However, the long transmission distances of lightpaths cause the poor signal-to-noise ratio (SNR), making the bit error rate (BER) of lightpaths cannot meet the requirement of forward error correction (FEC) at receivers [18]. Using all-optical amplifiers such as erbium-doped fiber amplifiers (EDFAs) to amplify optical signals is an energy-efficient way to compensate transmission losses in the optical domain, but the accumulated noise of amplifier spontaneous emission (ASE) and Doppler shift (DS) crosstalk also deteriorates the BER of lightpaths [19]. Therefore, lightpath regeneration is necessary to ensure the quality of transmission (QoT) in the SON [20]. The translucent optical payload architecture is most economical and feasible for SONs, which enables to increase the transmission reach of lightpaths with acceptable BER by optical-electrical-optical (OEO) regeneration. However, there is non-negligible energy consumption of OEO regeneration, mainly deriving from performing OEO conversion and digital signal processing (DSP) for traffic in lightpaths [21].

Regeneration routing can ensure the acceptable QoT by designating the regeneration nodes for lightpaths. Currently, there are many studies related to regeneration routing have been proposed to improve the energy efficiency of lightpath regeneration in TONs. In [22], C. Wan et al. proposed the mixed regenerator placement scheme for the regeneration routing in TONs, and the mixed placement of all-optical regenerators and OEO regenerators can reduce the overall energy consumption while ensuring transmission qualities of lightpaths in TONs. In [23], K. Walkowiak et al. proposed the regeneration routing for elastic TONs, and pointed out that using high-order modulation formats to improve the spectral efficiency of lightpaths requires designating more regeneration nodes, causing more energy consumption. Different from terrestrial network equipment having renewable power support, the recharge battery is the sole energy support for the low-orbit satellite in eclipse. Consuming the same size of battery energy at different DODs may have different effects on battery life, and deepening the DOD will aggravate battery aging. Unlike the regeneration routing reducing the overall energy consumption in TONs, reducing the discharge of the batteries at deep DOD to alleviate battery aging is even more important for the regeneration routing in SONs, which has few related studies. Based on the translucent optical payload architecture, this paper proposes energy-efficient regeneration routing (EE-RR) in SONs, which is to reduce the battery life consumption of lightpath regeneration. We define the maximum bypass hops (MBH) to ensure the BER requirement of lightpaths in SONs, considering the noise accumulation of ASE and DS crosstalk. Two greedy baselines of EE-RR are proposed in this paper, which are the regeneration routing scheme minimizing the number of regeneration nodes (RRS-MRN), and the regeneration routing scheme minimizing single satellite’s battery life consumption (RRS-MBL), respectively. Based on two baselines, we develop the regeneration routing scheme using genetic algorithms (RRS-GA) to improve the optimization ability of EE-RR. To our knowledge, this is the first research taking battery aging into account in lightpath regeneration in SONs.

The rest of this paper is organized as follows. Section 2 presents the theoretical model of SONs, including networking components, translucent optical payload architecture, MBH in lightpaths, energy consumption analysis, and energy support in satellites. Section 3 introduces two greedy baselines RRS-MRN and RRS-MBL, and RRS-GA is also developed in this section. The performance evaluation and numerical analysis are presented in Section 4. Finally, we conclude this paper and discuss the further researches in Section 5.

2. Theoretical model of SONs

This section first presents the components of SONs, and then introduces the translucent optical payload architecture. The calculation of the MBH in lightpaths is also given. Finally, the energy consumption and the energy support of satellites are analyzed. Some acronyms are listed in Table 1 in order of appearance in this paper.

Table 1. Acronym List

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2.1 Networking components

A system consisting of multiple satellites working cooperatively is the constellation, where all satellite orbits have the same altitude and the same inclination. Based on the circular orbit, the SON usually follows a uniform constellation. This paper represents a uniform constellation with five parameters {h₀, θ, N_orbit, N_sat, Δw}, where h₀ is the orbit height, θ is the orbit inclination angle, N_orbit is the number of orbits, N_sat is the number of satellites within each orbit, and Δw is the phase factor between adjacent orbits. Currently, the snapshot policy is commonly used to abstract the SON [24], where the SON topology is taken as a static snapshot at different moments, and the connectivity relationship of the SON is fixed within the snapshot duration. This paper models the physical SON topology under each snapshot as the bidiagraph G(V,E), where V denotes the set of LEO satellites, and E denotes the set of LISLs. In this paper, we set that the LISL connectivity relationships in SONs follow the typic mesh pattern [25]. As shown in Fig. 1, there are two types of LISLs in SONs, including intra-orbit LISLs and inter-orbit LISLs. The intra-orbit LISL is the laser link between two adjacent satellites in the same orbit. The relative position between satellites in the same orbit is fixed, so the distance of intra-orbit LISLs is constant. The inter-orbit LISL is the laser link between two adjacent satellites in neighboring orbits. The relative position between two adjacent orbits differs at different latitudes, causing the distance of inter-orbit LISLs to change over time.

Fig. 1. Schematic diagram of LISLs in SONs.

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2.2 Translucent optical payload architecture

The High thRoughput Optical Network (HydRON) vision of the European space agency (ESA) is to seamlessly extend terrestrial high-capacity optical network into space [26]. Some successful conclusions of internal assessments addressing various mission and system implementations have been presented in [27]. Referring to the HydRON, Fig. 2 presents the translucent optical payload architecture implementing transparent optical switching and OEO regeneration. Optical burst switching is applied in the translucent optical payload architecture, which is currently the most suitable optical switching technology for the SON [28]. The optical components of the translucent optical payload mainly include optical switching matrices called optical cross connect (OXC), optical amplifiers such as EDFAs, and optical multiplexers/demultiplexers. The electronic components of the translucent optical payload mainly include transponders and OEO regenerators. The transponder is a bidirectional device that, 1) provides the interface with the RF access traffic, 2) digitizes signals, 3) performs channel coding according to FEC, and 4) retransmits optical signals on the appropriate wavelength channels. The OEO regenerator performs the same operations as transponders. In particular, one OEO regenerator can be implemented by two back-to-back transponders, and using two back-to-back transponders can achieve lightpath regeneration in SONs. “All-optical transparency” in SONs can improve the energy efficiency of satellites while fulfilling high-throughput needs, and “OEO translucency” is also required to interface with the RF access and to regenerate the optical signal to avoid excessive optical SNR degradation after several bypass hops. OEO conversion is necessary for performing re-amplifying, re-shaping, and re-timing (3R) regeneration in optical networks [29]. In this context, the translucent optical payload currently is the most economical and reliable architecture for SONs [30], which relies on OEO regeneration at relay satellites to increase the transmission reach of lightpaths.

Fig. 2. Translucent optical payload architecture in SONs.

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For the SON using the translucent optical payload architecture, there are two ways for lightpaths passing through relay satellites, which are non-bypass and bypass, as shown in Fig. 3. Under non-bypass, the carried traffic of lightpaths is processed and forwarded by the on-board payload. In contrast, the lightpath under bypass allows the carried traffic to transparently pass through the relay satellite and doesn’t be processed by the on-board payload [31]. Lightpath bypass reduces the energy consumption of the traffic processing in the electronic domain. To ensure the acceptable QoT, OEO regeneration is necessary for lightpaths in SONs, and lightpaths cannot bypass regeneration nodes. EE-RR in SONs is to route lightpaths and designate the relay satellites with high energy efficiency as regeneration nodes of lightpaths to ensure the acceptable QoT.

Fig. 3. Different ways for lightpath passing though relay satellites, (a) lightpath non-bypass, (b) lightpath bypass.

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2.3 MBH of regeneration routing

Unlike the TON consisting of fixed-distance fiber links, there are LISLs with time-varying distances in the SON, so it is difficult to designate regeneration nodes based on the real-time transmission distances of lightpaths. In uniform constellations, satellite movements are regular, the distance variation repeats among LISLs, and the change range of LISL distances can be determined. We define MBH as the maximum number of relay nodes that lightpaths can bypass after OEO regeneration. The BER evaluation model for repeat LISLs with the minimum single-hop SNR is used to calculate the MBH of lightpaths, which ensures the acceptable QoT even in the worst case (investigating the worst case is the common research method for the SON consisting of LISLs with time-varying distances [32]).

The SNR of the lightpath is closely related to its distance, and the long-distance lightpath passes through many LISLs and accumulates a lot of noise power, which causes poor SNR. The BER evolution model proposed in [33] is to abstract the optical channel into repeated links with multiple hops of amplify relays, and the noises of optical signals are accumulated along hop increasing until it cannot meet the BER requirement. In this paper, we set the photodetector responsivity as R = 1 A/W, and only ASE noise and crosstalk noise are considered at the satellite optical switch [34]. The single-hop SNR in the lightpath is given as Eq. (1), where G is the amplify gain, P_s is the power of the main signal, and δ²_ASE and δ²_cros are the variances of ASE noise and crosstalk noise, respectively.

(1)$$SN{R_1} = \frac{{{{(G \times R \times {P_s})}^2}}}{{{\delta ^2}_{ASE} + {\delta ^2}_{cros}}}$$

The variance of ASE noise is given in Eq. (2), where n_sp is the spontaneous emission factor, h is the Plank’s constant (6.6261 × 10⁻³⁴), f_c is the carrier frequency, and B_e is the electrical bandwidth.

(2)$${\delta ^2}_{ASE} = 4 \times G \times {P_s} \times {n_{sp}} \times h \times {f_c} \times (G - 1) \times {B_e}$$

Crosstalk noise in LISLs is mainly caused by DS, and current research shows that the peaks of DS in the LISLs following the mesh pattern are relatively small [35] (the mesh pattern is the most likely LISL layout to be implemented, since it results in the least free space loss and small DS). This paper assumes that the accurate wide-range frequency tracking and the advanced DS compensation methods are processed in OEO regeneration to recover the carrier frequency of lightpaths in SONs. J. Ma et al. have established the expression of the crosstalk noise power at the satellite optical switch in [32], A. D. Barman et al. further simplified the normalized the relative intensity noise power [36], and the expression of δ²_cros is given as Eq. (3), where N is the number of LISLs at the satellite optical switch, W is the number of wavelengths per LISL, Δν is the laser line-width, c is the light velocity, λ is the central wavelength, Δλ is the wavelength difference caused by DS, and ɛ is the corsstalk level at the optical switch. Taking S(f) as the power spectral density (PSD) of the main signal and F(f) as the filter function, crosstalk level ɛ can be expressed by Eq. (4), where f_d is the frequency difference caused by DS.

(3)$${\delta ^2}_{cros} = \frac{{N \times (W - 1) \times \varepsilon }}{\pi }[\arctan (\frac{{{B_e} + c \times \Delta \lambda /{\lambda ^2}}}{{\Delta \nu }}) + \arctan (\frac{{{B_e} - c \times \Delta \lambda /{\lambda ^2}}}{{\Delta \nu }})] \times {(G \times {P_{in}})^2}$$

(4)$$\varepsilon = \frac{{\int_{ - \infty }^\infty {S(f - {f_d})|H(f){|^2}df} }}{{\int_{ - \infty }^\infty {S(f)|H(f){|^2}df} }}$$

This paper assumes the PSD and filter function are both typical Lorentz functions, which are given in Eqs. (5) and (6), respectively.

(5)$$S(f) = \frac{{2 \times {P_{in}}/(\pi {B_s})}}{{1 + {{(2f/{B_s})}^2}}}$$

(6)$$H(f) = \frac{1}{{1 + {{(2f/{B_f})}^2}}}$$

A. B. Carlson et al. have pointed out that the total noise variances tend to the multiplied trend after multiple hops of repeated links [37]. Therefore, the SNR at the M_th hop can be simplified by Eq. (7), and the BER at the M_th hop can be calculated by Eq. (8). $(7)$$SN{R_M} = \frac{{SN{R_1}}}{M}$$$ $(8)$$BE{R_M} = \frac{1}{2}erfc(\frac{{\sqrt {SN{R_M}} }}{{2\sqrt 2 }}) = \frac{1}{2}erfc(\frac{{\sqrt {SN{R_1}} }}{{2\sqrt 2 \times \sqrt M }})$$$

Based on the above analysis, the configurations of LISLs (such as signal power, electrical bandwidth, spontaneous emission factor, carrier frequency, laser line width, wavelength number, channel spacing, and so on) and the constellation settings (such as LISL distance) directly determine the value of single-hop SNR. In the worst case that there is the minimum single-hop SNR in the repeated LISL, the BER of the lightpath at the regeneration node can be considered as a function of the number of bypass hops M, as given by Eq. (8). We denote BER_req as the required BER under the limit of FEC in LISLs, SNR_min as the fixed value of the minimum single-hop SNR in repeated LISLs, and the MBH in lightpaths is given by Eq. (9).

(9)$$MBH = \max \{ M|\frac{1}{2}erfc(\frac{{\sqrt {SN{R_1}} }}{{2\sqrt 2 \times \sqrt M }}) \le BE{R_{req}}\}$$

2.4 Energy consumption analysis

Let P_A denote the energy consumption of the optical amplifier EDFA. This paper assumes that inter-orbit LISLs and intra-orbit LISLs have different fixed gains to compensate for losses in the optical domain (there are different distance ranges of inter-orbit LISLs and intra-orbit LISLs), and the energy consumption of EDFA is calculated as Eq. (10) [38], where η is the energy conversion efficiency of EDFA, and W is the number of wavelengths per LISL. The configuration of the LISL with the minimum single-hop SNR exceeds the actual gain requirement of LISLs in most cases, and the excess gain is taken as the link margin of LISLs to ensure link reliability.

(10)$${P_A} = \frac{1}{\eta } \times W \times {P_s} \times (1 - \frac{1}{G})$$

Let P_R denote the energy consumption of regeneration devices, which varies depending on the carried traffic in the regeneration lightpath. Equation (11) describes P_R as a function of lightpath’s traffic [39–41], where R_baud is the baud rate in the lightpath, w₁ is the energy scaling factor related to OEO conversion, and w₂ is a constant related to the operation of the laser resource and analog components.

(11)$${P_R} = {w_1} \times {R_{baud}} + {w_2}$$

Let P_E denote the energy consumption of the electronic processor, which has an exponential relationship with the size of traffic carried by the lightpath [42], as calculated by Eq. (12), where R_bit is the bit rate in the lightpath, ξ and ɛ are two constant parameters in the electronic processor.

(12)$${P_E} = \xi \times {({R_s})^\varepsilon }$$

If the lightpath passes through the on-board payload transparently (lightpath bypass), it causes little energy consumption in optical amplifiers; otherwise, it requires OEO conversion for total data in lightpaths (lightpath regeneration), which causes non-negligible energy consumption of regenerator devices and the electronic processor. For the translucent optical payload architecture, the control data for switch controllers only accounts for a small part of the total traffic carried by lightpaths. For simplicity, this paper assumes that the energy consumption of the switch controller is a constant P_SC.

Moreover, electronic traffic grooming is necessary at source and destination satellites of lightpaths [43], which requires OE/EO conversion to interface with the RF access. The source satellite and destination satellite are both considered as the regeneration nodes of lightpaths to approximate the energy consumption of electronic traffic grooming. In this paper, the energy consumption of driving the RF antenna is assumed as a constant P_RF, the energy consumption of driving the laser terminal is assumed as a constant P_LISL, and the energy consumption change of communication links are not considered (Y. Yang et al. have pointed out that the energy consumption change of communication links caused by traffic variation is negligible for satellite’s total energy consumption [12]). This paper sets that, each satellite needs to drive the laser terminal to establish LISLs with fixed adjacent satellites, and only the source and destination satellites need to drive the RF antenna.

In addition to the energy consumption of lightpaths, supporting the basic functions of satellite operation infrastructures (such as maintaining satellite altitude, rotating solar panels, supporting satellite navigation, and so on) also causes energy consumption, and this paper denotes P_BF as the energy consumption of those basic functions, which is assumed as a constant.

2.5 Energy support of satellites

Generally, LEO satellites are powered by solar panels and rechargeable batteries. By querying ephemeris, the relative position of LEO satellites to sunlight can be determined in advance. When the satellite moves in front of the earth (satellite in sunlight), solar panels can recharge the battery while powering satellite operation. When the satellite moves in the back of the earth (satellite in eclipse), the earth blocks sunlight from reaching the solar panels, and the satellite can only be powered by battery discharge.

For lithium-ion batteries that are commonly used in current satellites, the cycle life is affected by several factors, including DOD, discharge rate, temperature, etc. This paper only considers the effect of DOD on the battery life. DOD refers to the ratio of the current energy consumption to the battery energy capacity [44], as given in Eq. (13), where D(t) denotes the DOD at current moment t, C_max is the battery capacity, and C(t) is the residual battery energy at time t. J. P. Fellnera et al. have found the relationship between the total cycle life of batteries and DOD [45]. Let L_total denote the total cycle life of batteries. Assume that the battery always be discharged from a DOD of 0 to a DOD of 1, the expression of total cycle life L_total is given by Eq. (14), where A and B are constants that depend on battery specification. The battery life consumption can be considered as the change of residual cycle life before and after battery discharge.

(13)$$D(t) = \frac{{[{C_{\max }} - C(t)]}}{{{C_{\max }}}}$$

(14)$${L_{\textrm{total}}} = {10^{B - A}}$$

Existing studies have investigated the battery life consumption rate f(D) at different DOD [12–16], as given by Eq. (15). Let ΔL denote the battery life consumption. When the battery is discharged from DOD 0 to DOD D, the amount of consumed cycle life can be calculated by Eq. (16).

(15)$$f(D) = {10^{A \times (D - 1)}} \times (1 + A \times \ln 10 \times D)$$

(16)$$\Delta L = D \times {10^{A \times (D - 1)}}$$

Based on the above, consuming the same size of battery energy at different DODs may have different effects on the battery life, and deepening the DOD will aggravate battery aging.

3. Design of EE-RR

To ensure the acceptable QoT, OEO regeneration is necessary for lightpaths in SONs. Regeneration routing is to route lightpaths and designate regeneration nodes of lightpaths. The traffic grooming is also an important issue for the SON, which is to add the small-granularity access traffic into the large-granularity wavelength (or drop access traffic from wavelength). Due to the limited space, the energy-efficient traffic grooming of SONs is not covered in this paper, and only the wavelength-granularity bandwidth request is considered in lightpaths from source satellites to destination satellites.

Consuming the same size of battery energy at different DODs may have different effects on the battery life, and deepening the DOD will aggravate battery aging. Instead of reducing the total energy consumption of lightpath regeneration, EE-RR is to reduce the energy consumption of batteries at the deep DOD. This paper assumes that OEO regeneration can achieve perfect SNR recovery for lightpaths. Figure 4 shows three different lightpaths between the same satellite pair, where the MBH of the lightpath is assumed as two, and the satellite in sunlight can use the solar panels for power and doesn’t consume battery life. For easy visual comparison, only the LISLs occupied by lightpaths are presented in Fig. 4, which are represented by red lines. There are different LISLs used to establish lightpath-1 and lightpath-2. In lightpath-1, one satellite with battery DOD at 80% in eclipse is designated as the regeneration node. In lightpath-2, one satellite with battery DOD at 60% in eclipse is designated as the regeneration node. By Eqs. (13–16), regenerating lightpath-1 aggravates the battery aging more severely than regenerating lightpath-2. There are the same LISLs used to establish lightpath-2 and lightpath-3. In lightpath-3, one satellite with battery DOD at 20% in eclipse and one satellite in sunlight are designated as regeneration nodes. Lightpath-3 using one more regeneration node causes less battery life consumption than lightpath-1 and lightpath-2, because the relay satellite in sunlight is designated as the regeneration node, which can be powered by solar panels and doesn’t cause battery life consumption.

Fig. 4. Different lightpaths in SONs.

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By comparison above, different lightpaths have significant differences in battery life consumption of lightpath regeneration. Reducing the use of batteries at the deep DOD to power OEO regeneration can improve the energy efficiency of satellites, which is the purpose of EE-RR. Some notations related to EE-RR are listed in Table 2. The objective of EE-RR is to reduce the battery life consumption of lightpath regeneration, as given in Eq. (17). However, the specific numerical value of battery life consumption cannot be directly obtained within proceeding EE-RR, because the battery life consumption corresponds to the time-domain integral of life consumption rate at different DOD. Considering that the battery at a deep DOD consumes lifetime seriously, this paper uses the battery DOD and parameters related to energy consumption to approximate the optimization objective of EE-RR, as given in Eq. (18), where I_v is the set of lightpaths that have designated satellite v as regeneration node, τ is the snapshot duration, R_i is the size of traffic of lightpath i∈I_v, and y_v is a binary variable that indicates satellite v is in sunlight or not. When the satellite is in sunlight, it can directly use the solar panel for power supply and avoid consuming battery life, and binary variable y_v is set as 0 at this time, otherwise, y_v is set as 1.

(17)$$\min \textrm{ }f({P_r}) = \sum\limits_{v \in R{N_r}} {\Delta {L_v}}$$

(18)$$\min \textrm{ }f^{\prime}({P_r}) = \sum\limits_{v \in R{N_\textrm{r}}} {{y_v} \times \{ {D_v} + \frac{{[{w_2} + \sum\limits_{i \in {I_v}} {{R_i} \times {w_1} + \xi \times {{({R_i})}^\varepsilon }} ]}}{{{C_{\max }}/\tau }}\} }$$

Table 2. Notations of EE-RR

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Implementing EE-RR consists of three main steps: 1) finding a lightpath from request’s source satellite to destination satellite; 2) designating some relay satellites as regeneration nodes of the lightpath to ensure acceptable BER; 3) assigning wavelengths in the occupied LISLs of the lightpath. For path finding of EE-RR, traditional algorithms such as the Shortest Path (SP) algorithm and the K Shortest Paths (KSP) algorithm can be used. This paper emphasizes the effect of bypass hops on lightpaths’ transmission qualities, and the shortest path of SP and KSP algorithms refers to the lightpath consisting of least LISLs. When using the KSP algorithm and two baselines for EE-RR, multiple paths with different LISL compositions are obtained as candidate lightpaths. After using RRS-MRN or RRS-MBL to designate regeneration nodes for each candidate lightpath, we can calculate the objective value of each candidate lightpath, and the candidate lightpath with the minimum objective value is taken as the final output regeneration lightpath. For the wavelength assignment of EE-RR, the regeneration node can achieve wavelength conversion while recovering SNRs of lightpaths, so the wavelength consistency constraint only needs to be satisfied between adjacent regeneration nodes of lightpaths, and the wavelength can be changed after the lightpath passing through each regeneration node. In this paper, the First-Fit (FF) algorithm is used to assign the wavelength of the lightpath between adjacent regeneration nodes. The KSP algorithm can find multiple feasible lightpath between the same node pair. After using baselines to designate regeneration nodes of each feasible lightpath found by KSP, the lightpath having the minimum f’ is taken as the final output of EE-RR. Next, we introduce two baselines, respectively.

3.1 Baseline RRS-MRN

Some researches on regeneration routing for TONs [22,23] indicate that, the energy consumption of lightpath regeneration can be effectively reduced by reducing the number of regeneration nodes in the lightpath. Referring to the researches for TONs, baseline RRS-MRN is to establish lightpaths using the minimum number of regeneration nodes of each lightpath in SONs. RRS-MRN is detailed as Algorithm 1. RRS-MRN can minimize the energy consumption of the lightpath having the given LISL composition. However, battery life consumption cannot be quantified only based on energy consumption, consuming the same size of battery energy at different DODs may have different effects on the battery life, and deepening the DOD will aggravate battery aging.

To minimize the number of regeneration nodes, the lightpath under RRS-MRN processes OEO regeneration only after each time bypassing M relay satellites fixedly, as detailed in Steps 6-8. RRS-MRN minimizes the number of regeneration nodes while ensuring the acceptable QoT in lightpaths.

Algorithm 1. RRS-MRN

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3.2 Baseline RRS-MBL

Greedy baseline RRS-MBL is to choose the satellite having the slightest battery DOD among the M-hops satellites following the previous regeneration node as the next regeneration node, which can minimize single satellite’s battery life consumption, as detailed in Algorithm 2.

Algorithm 2. RRS-MBL

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In Step 6, V’ is the set of relay satellites that can be chosen as regeneration nodes for the lightpath after the h_th hop. Under RRS-MBL, the number of relay satellites that each time lightpath bypassing may be less than MBH M. For the lightpath that has been regenerated at the h_th hop, taking the relay satellite at the (h + M + 1)_th hop as the regeneration node may cause more serious battery life consumption than the relay satellite before the (h + M + 1)_th hop.

3.3 RRS-GA

Many studies on the TON have indicated that minimizing the cost of regeneration routing is a classical NP-hard problem [46]. For the SON, different battery DOD of satellites further increases the complexity of EE-RR. As lightpath comparison in Fig. 4, blindly reducing the number of regeneration nodes cannot effectively reduce overall battery life consumption, because the different relative position to sunlight and the different battery DOD make that each satellite has different energy efficiency. In addition, the LISL connectivity relationship of the SON follows the 4-regular topology, where many lightpaths consisting of different LISLs can be established between the same satellite pair. The diversities of feasible LISLs and selectable regeneration nodes in lightpaths form the large-scale solution domain of EE-RR, so it is difficult to achieve the ideal optimization solution only relying on two baselines.

Genetic algorithms have a strong search ability through mutation and crossover mechanisms to avoid solutions into local optimal, and the idea of fitness evaluation ensures the convergence of the optimization objective. In addition, compared with other intelligence algorithms such as ant colony algorithms, the reasonable design of gene mutation and gene crossover in genetic algorithms can limit variables in permitted range to meet the problem constrains while generating more candidate solutions, simplifying search process. In this paper, we apply two baselines to gene mutation and gene crossover in genetic algorithms, and design RRS-GA to improve the optimization ability of EE-RR. Gene mutation and gene crossover using two baselines ensure that RRS-GA can provide feasible solutions for EE-RR. The flowchart of RRS-GA is shown in Fig. 5, where ψ is the maximum number of generation iterations. When the number of population iterations reaches ψ, the individual with the highest fitness is taken as the final output of RRS-GA.

Fig. 5. Flowchart of RRS-GA.

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Genetic algorithms have been used to solve the regeneration node placement problem (designating regeneration nodes for a given lightpath with the fixed link composition) in TONs. In [47], Z. Zhu et al. have proposed a genetic algorithm to reduce the number of regeneration nodes while ensuring transmission quality, which designates regeneration nodes for each given lightpath independently and does not involve adjusting the link composition of lightpaths. For SONs, the lightpath with different LISL compositions may pass through the satellites with different battery DODs, and adjusting the routing of each lightpath may change the lightpath’s LISL composition and have different effects on battery life consumption. Therefore, our proposed RRS-GA takes into account both the LISL composition and the regeneration nodes of each lightpath. Considering that establishing regeneration lightpaths for multiple connection requests simultaneously will greatly enlarge the solution domain of the problem, RRS-GA is to implement the regeneration routing for the single connection request. For RRS-GA, one solution can be considered as a two-dimensional vector X = [RL,RN] consisting of two one-dimensional vectors RL and RN, which sequentially store used LISLs RL and occupied regeneration nodes RN in the lightpath. To ensure the solution feasibility, vectors RL and RN must satisfy two main constraints, where RL must ensure the lightpath is connected from the source satellite to the destination satellite, and RN must ensure the number of consecutive bypass hops in the lightpath cannot exceed MBH. The difference between RRS-GA and baselines is that the baseline optimizes the entire lightpath independently. RRS-GA divides a long-distance lightpath into multiple different short-distance lightpaths and optimizes them respectively with different baselines, and finally evaluates the overall performance of the long-distance lightpath consisting of these short-distance lightpaths. We take Eq. (18) as the optimization objective of RRS-GA to approximate the extent of battery life consumption of lightpath regeneration in SONs. Some related concepts of RRS-GA are introduced as follows.

Gene coding: In RRS-GA, each solution is coded as one individual, and all individuals form the population. As shown in Fig. 6, the LISLs in the lightpath from source satellite to destination satellite are sequentially coded into vector RL, and the regeneration nodes in the lightpath are sequentially coded into vector RN. The amplifying nodes in Fig. 6 refer to the satellite nodes in the lightpath that are transparently passed through (bypass), and the optical signal of the lightpath only processes all-optical amplify at these nodes without OEO conversion. The energy consumption of lightpaths at amplifying nodes is negligible for the regeneration routing.

Fig. 6. Gene coding in RRS-GA.

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Population initialization: The initial population of RRS-GA is formed by the solutions generated using two baselines and KSP algorithm. First, the KSP algorithm is used to find multiple lightpaths between source and destination satellites. Next, randomly choosing a baseline to designate the regeneration nodes of each lightpath output by KSP. Using KSP to find paths can ensure that lightpaths’ LISL composition meets the connection requirement of regeneration routing. Using a baseline to designate regeneration nodes for individuals of RRS-GA guarantees that the lightpath meets MBH requirements. Population initialization in RRS-GA is detailed as Algorithm 3.

Algorithm 3. Population initialization

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In Step 4, two baselines RRS-MRN and RRS-MBL are used to designate regeneration nodes in K lightpaths for request r. The KSP algorithm ensures the basic diversity of individuals in the initial population.

Selection: Some individuals are chosen as parent individuals to generate child individuals by gene mutation and gene crossover. ɛ-greedy is used to choose parent individuals from the current population, where the individual is chosen as the parent of the next generation with a probability of (1-ɛ). A small value of ɛ makes individuals have a greater probability of being chosen as parent individuals to generate child individuals, which can increase the diversity of the population and expand the search domain of RRS-GA. In this paper, we set ɛ=0.2 to ensure the population diversity. Each parent individual has a certain probability to conduct gene mutation and gene crossover. This paper set the probability of gene mutation as Pm = 0.01, and the probability of gene crossover as Pc = 0.1.

Gene mutation: Gene mutation is essentially to adjust the LISL composition and regeneration nodes in the part of the existing solution. Using KSP and a baseline to adjust the part of the lightpath between two regeneration nodes can ensure that the new lightpath configuration still satisfies the lightpath connection requirement and MBH requirement. As shown in Fig. 7, for one given solution X_s,d= [RL_s,d,RN_s,d] (s and d are the source and destination satellites of lightpath P_s_,d corresponding to X_s,d), gene mutation randomly choose two intermediate regeneration node v1 and v2 to divide solution X_s,d= [RL_s,d,RN_s,d] into three parts X_s,v₁= [RL_s,v₁,RN_s,v₁], X_v_1,v2= [RL_v_1,v2,RN_v_1,v2], and X_v_2,d= [RL_v_2,d,RN_v_2,d]. Gene mutation uses KSP and one baseline to obtain one new lightpath configuration X’_v_1,v2= [RL’_v_1,v2,RN’_v_1,v2] from node v1 to node v2, and X’_v_1,v2= [RL’_v_1,v2,RN’_v_1,v2] is used to replace X_v_1,v2= [RL_v_1,v2,RN_v_1,v2] while remaining X_s,v₁= [RL_s,v₁,RN_s,v₁] and X_v_2,d= [RL_v_2,d,RN_v_2,d] unchanged. For X_s,v₁= [RL_s,v₁,RN_s,v₁], RL_s,v₁ meets the connection requirement from source satellite s to regeneration node v1, and RN_s,v₁ meets the MBH requirement. For X’_v_1,v2= [RL’_v_1,v2,RN’_v_1,v2], RL’_v_1,v2 meets the connection requirement from regeneration node v1 to regeneration node v2, and RN’_v_1,v2 meets the MBH requirement. For X_v_2,d= [RL_v_2,d,RN_v_2,d], RL_v_2,d meets the connection requirement from regeneration node v2 to destination satellite d, and RN_v_2,d meets the MBH requirement. Therefore, combining three parts X_s,v₁, X’_v_1,v2 and X_v_2,d can generate the new solution X’_s,d= [RL’_s,d,RN’_s,d], where RL’_s,d meets the connection requirement from source satellite s to destination satellite d, RN’_s,d meets the MBH requirement. Gene mutation in RRS-GA is detailed in Algorithm 4.

Algorithm 4. Gene mutation

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Fig. 7. Gene mutation in RRS-GA.

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Algorithm 4 uses KSP algorithm and two baselines to change the LISLs and regeneration nodes in part of the original lightpath, as detailed in Steps 2-6.

Gene crossover: Gene crossover is essentially to exchange the LISL composition and regeneration nodes between two individuals having the same regeneration nodes (cannot be source satellite or destination satellite). As shown in Fig. 8, for two given parent individuals X¹_s,d= [RL¹_s,d,RN¹_s,d] and X²_s,d= [RL²_s,d,RN²_s,d] having the same regeneration node v, we divide X¹_s,d= [RL¹_s,d,RN¹_s,d] into two parts X¹_s,v= [RL¹_s,v,RN¹_s,v] and X¹v_,d= [RL¹v_,d,RN¹v_,d], and divide X²_s,d= [RL²_s,d, RN²_s,d] into two parts X²_s,v= [RL²_s,v,RN²_s,v] and X²v_,d= [RL²v_,d,RN²v_,d]. Gene crossover exchanges the lightpath configurations between X¹_s,d= [RL¹_s,d,RN¹_s,d] and X²_s,d= [RL²_s,d,RN²_s,d] to generate two new solutions X’¹_s,d= [RL’¹_s,d,RN’¹_s,d] and X’²_s,d= [RL’²_s,d,RN’²_s,d]. RL’¹_s,d consists of two parts RL¹_s,v and RL²v_,d. RL’²_s,d consists of two parts RL²_s,v and RL¹v_,d. RN’¹_s,d consists of two parts RN¹_s,v and RN²v_,d. RN’²_s,d consists of two parts RN²_s,v and RL¹v_,d. Same as the analysis on gene mutation, RL’¹_s,d and RL’²_s,d both meet the connection requirement from source satellite s to destination satellite d, and RN’¹_s,d and RN’²_s,d both meet the MBH requirement. Gene crossover is detailed as Algorithm 5.

Algorithm 5. Gene crossover

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Fig. 8. Gene crossover in RRS-GA.

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Gene crossover can only occur between two parent individuals having the same regeneration node (expect source and destination satellites). Two parent individuals exchange their lightpath configurations after the same regeneration node, which guarantees that child individuals’ lightpaths both can establish the connection from source satellite to destination satellite, and ensures that the number of hops between adjacent regeneration nodes in child individuals’ lightpaths doesn’t exceed MBH.

Fitness assessment: In population iteration, parent and child individuals having high fitness are preferred to be retained to the next generation population. the approximate optimization objective calculated by Eq. (18) is used to evaluate the fitness of parent and child individuals. Individual X with the smaller f’(X) has the higher fitness in generation merge, and it is preferred to be chosen retained to the next population. The fitness of individual X = [RL, RN] is given by Eq. (19), where Q denotes the population consisting of each individual, and RL and RN denote the set of LISLs and regeneration nodes used in two vectors RL and RN, respectively.

(19)$$fitness(\textrm{X} = [{RL},{RN}]) = \frac{{\sum\limits_{v \in RN} {{y_v} \times \{ {D_v} + \frac{{[{w_2} + \sum\limits_{i \in {I_v}} {{R_i} \times {w_1} + \xi \times {{({R_i})}^\varepsilon }} ]}}{{{C_{\max }}/\tau }}\} } }}{{\sum\limits_{[{RL^{\prime}},{RN^{\prime}}] \in \textrm{Q}} {\sum\limits_{v^{\prime} \in RN^{\prime}} {{y_{v^{\prime}}} \times \{ {D_{v^{\prime}}} + \frac{{[{w_2} + \sum\limits_{i \in {I_{v^{\prime}}}} {{R_i} \times {w_1} + \xi \times {{({R_i})}^\varepsilon }} ]}}{{{C_{\max }}/\tau }}\} } } }}$$

Generation merge: After calculating the fitness of the original individuals and newly generated child individuals under the current generation, a fixed number of individuals are retained into the next generation by roulette, and the fitness of an individual is its probability of being chosen in roulette.

3.4 Time complexity analysis

The time complexities of RRS-MRN and RRS-MBL are O(K*H) and O(K*H²), respectively, where K is the number of the candidate lightpaths, and H is the maximum number of hops in candidate lightpaths. Based on the time complexities of RRS-MRN and RRS-MBL, the time complexities of population initialization, gene mutation, and gene crossover in RRS-GA are all O(K*|V|³+ K*H²), where |V| is the number of satellites in the SON. The time complexity of RRS-GA is O(Λ*ψ*(K*|V|³+ K*H²)), where Λ is the number of population iterations, and ψ is the number of individuals under each generation. RRS-GA can achieve high-performance solutions by emulating population evolution. However, the population iterations and individual operations make a high time complexity in RRS-GA.

4. Performance evaluation

In this section, the numerical results and analysis of EE-RR are presented. Walker Delta constellation Starlink is used to simulate the SON to provide satellite communication coverage, where there are 72 orbit planes with 22 LEO satellites per orbit. We simulate the SON to work 24 hours from 0:00 a.m., January 1, 2024, Beijing time. The inclination of each orbit plane in Starlink is 53°, and we assume that there is no LISL out of operation due to link pointing difficulty. Some simulation settings of Starlink constellation and satellite energy consumption are listed in Table 3.

Table 3. Simulation settings

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4.1 Numerical analysis related to MBH

In SONs, the distance of the inter-orbit LISL is time-varying while that of the intra-orbit LISL is constant. In addition to the wavelength difference caused by DS, the time-varying distance of the inter-orbit LISL causes changes in space free loss. Therefore, it is necessary to analyze the variation range of the single-hop SNR in LISLs to determine the MBH of lightpaths.

For the worst case that the lightpath has the minimum single-hop SNR in each LISL, we can calculate the values of MBH according to the BER requirement of FEC. This paper sets that the OOK modulation is applied in LISLs, and the BER performance under different single-hop SNR SNR₁ and repeated hops M is shown in Fig. 9. We set the BER requirement of FEC as SER_req= 1 × 10⁻⁵, and the MBH within different ranges of the single-hop SNR in LISLs are listed in Table 4.

Fig. 9. BER under different single-hop SNRs and repeated hops.

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Table 4. MBH under different SNRs

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After obtaining the MBH under each range of single-hop SNR, we need to determine the variation of single-hop SNR in inter-orbit LISLs. Figure 10(a) shows the time-varying distances of three different inter-orbit LISLs, where the distance range of inter-orbit LISLs in Starlink is from 390.79349 Km to 620.66681 Km. LISL’s distance directly determines its free space loss, and Fig. 10(b) shows free space loss L_sp in inter-orbit LISLs at different moments, where the central wavelength of LISLs is f₀= 1550 nm. We can calculate the wavelength difference caused by DS based on the distance changes of inter-orbit LISLs, as shown in Fig. 10(c). As we mentioned earlier, the minimum single-hop SNR is directly determined by the configuration of LISLs. In this part, we give a set of LISL configuration parameters to analyze the variation of single-hop SNR. In single-hop inter-satellite communication, we set that the received power of the LISL is P_in= 1 × 10⁻²mW at the shortest distance (L_sp= 250.01651 dB). The fixed gain of EDFA is set as G₁= 10 in the inter-orbit LISL, and that of EDFA is set as G₂= 200 in the intra-orbit LISL (because intra-orbit LISLs have a longer distance than inter-orbit LISLs in Starlink). The number of wavelengths of each LISL is N = 8, and the channel spacing is f_d= 400 GHz. The electrical bandwidth is B_e= 6.5 GHz, the laser line width is B_l= 0.8B_e, the filter-3 dB bandwidth is B_f= 10 GHz, and the signal-3 dB bandwidth is B_s= 0.5B_f. The range of the single-hop SNR in inter-orbit LISLs is shown in Fig. 10(d). Benefit from the dense distribution of orbit planes and the low orbit inclination in Starlink, inter-orbit LISLs have less free space loss and DS, and the variation of the single-hop SNR in the inter-orbit LISL is relatively small. For intra-orbit LISLs, satellites are relatively stationary with each other. In Starlink, the distance of each intra-orbit LISL is a constant as d = 1269.92 Km, and there is a fixed value of free space loss as L_sp= 264.066542 dB. The single-hop SNR in the intra-orbit LISL is SNR₁= 24.816445 dB.

Fig. 10. Simulation results of inter-orbit LISLs, (a) link distances of inter-orbit LISLs, (b) free space loss of inter-orbit LISLs, (c) wavelength difference caused by DS in inter-orbit LISLs, (d) single-hop SNR in inter-orbit LISLs.

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Although there is no DS in intra-orbit LISLs, the longer distance of intra-orbit LISLs requires a larger gain of EDFA than inter-orbit LISLs, which generates the more serious ASE noise to deteriorate the single-hop SNR. By numerical comparison, the single-hop SNR in intra-orbit LISLs is smaller than that in inter-orbit LISLs, and the minimum single-hop SNR for lightpath bypass is SNR₁= 24.816445 dB. Therefore, in the SON under the LISL configuration parameters given above, we can get that the lightpaths’ MBH is 4 by referring to the data in Table 4.

4.2 Performance evaluation of regeneration routing

In the previous part, the variation of single-hop SNR in lightpaths is analyzed under one set of specific LISL configuration parameters. In this part, we compare the performance of EE-RR under different MBHs (adjusting the LISL configuration can change the minimum value of the single-hop SNR, further achieving different MBH).

The energy consumption of all-optical amplify is much less than that of OEO regeneration, and this paper neglects the energy consumption of all-optical amplify. For regeneration devices, the energy-efficient optical transponder is considered, where w₁ and w₂ are equal to 0.105W/Gbps and 21.5W [41], respectively. This paper assumes that there is a fixed data rate (bit rate) configured in each lightpath, and each lightpath occupies one wavelength. The energy consumption of regeneration devices changes with the number of regeneration lightpaths. Assuming that the bit rate of each wavelength is 10Gbps, we can get the energy consumption of regeneration devices in lightpaths is not less than 22.55W, and the energy consumption of traffic processing in lightpaths is not less than 25.12W. For performance evaluation, this paper sets that each snapshot has the fixed number of requests randomly distributed in the SON, and each request is established at the snapshot’s start time and removed at the snapshot’s end time. Three degrees (slight, moderate, and heavy) of network load are simulated for performance evaluation. The numbers of connection requests are set as 500, 800, and 1000 under three network loads respectively. We assume that the relative position of the satellite to sunlight is fixed within each snapshot, i.e., the satellite is always in sunlight or eclipse within each snapshot’s duration.

In this paper, service blocking means that there are not enough idle wavelengths to establish lightpaths for some connection requests. Under moderate and heavy load cases, different regeneration routing schemes may cause different probabilities on service blocking, and the numbers of established lightpaths are also different. Comparing the battery life consumption under establishing different numbers of lightpaths cannot provide a convincing performance evaluation. Therefore, we discuss the slight load case separately from the moderate and heavy load cases, which can provide an independent comparison on the battery life consumption under the premise of establishing the same number of lightpaths, making the performance evaluation more convincing. Firstly, the slight network load without request blocking is simulated in the SON, where 500 requests are generated under each snapshot to evaluate the performance of EE-RR. We compare the performances of two baselines using two path-finding algorithms SP and KSP, where the maximum number of lightpaths found by the KSP algorithm is set as 20. Assuming that different MBH of lightpaths can be achieved by adjusting the configuration parameters of LISLs, the battery life consumption, the average number of regeneration nodes, and the average number of occupied LISLs in lightpaths with different MBHs are shown in Figs. 11(a-c), respectively.

Fig. 11. Simulation results of two baselines in the SON under the slight network load, (a) battery life consumption of lightpaths, (b) average number of regeneration nodes of lightpaths, (c) average number of LISLs occupied by lightpaths.

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Obviously, the increase of MBH can significantly reduce the battery life consumption and the number of regeneration nodes in lightpaths. Two baselines using KSP perform better than using SP in terms of battery life consumption, which confirms our analysis in Section 3. In addition, RRS-MBL using KSP has a lower battery life consumption than RRS-MRN using KSP when MBH exceeds 5 hops, and RRS-MBL using SP has a lower battery life consumption than RRS-MRN using SP when MBH exceeds 6 hops. When the MBH is 4 hops, RRS-MRN reduces battery life consumption by 5.61% compared with RRS-MBL; but when the MBH is 7 hops, RRS-MBL reduces battery life consumption by 5.61% compared with RRS-MRN. For any MBH, RRS-MBL always uses more regeneration nodes in lightpaths than RRS-MRN, and the performance of lightpaths with MBH exceeding 6 hops confirms that blindly reducing the number of regeneration nodes cannot effectively reduce overall battery life consumption. It should be noted that, we cannot make a general judgment that the battery life consumption of RRS-MBL is gradually less than that of RRS-MRN with the increase of MBH in each lightpath, because there are greatly different distributions of source and destination satellites in different lightpaths. For the SON under the slight network load, there are sufficient idle wavelengths in LISLs, and using KSP can find multiple lightpaths with different LISL compositions between the same satellite pair. There is less battery life consumption of lightpaths under baselines using KSP compared to baselines using SP, and we can find that there is no significant difference in the average number of LISLs used in lightpaths between two baselines using SP and KSP, as shown in Fig. 11. Therefore, under the slight network load, different lightpaths consisting of the similar number of LISLs can be established between the same satellite pair, and using KSP for path finding of EE-RR doesn’t cause significant request blocking.

Figure 12 presents the performance of RRS-GA under different numbers of individuals and generations in the SON under the slight network load, where N__ind denotes the number of individuals, the probability of gene mutation is set as 0.01, the probability of gene crossover is set as 0.1, MBH is set as 5 hops, and the maximum number of generation iterations is ψ=25. Table 5 lists the performance value of two greedy baselines RRS-MRN and RRS-MBL using SP and KSP, which is used for the performance comparison with RRS-GA. By numerical comparison, RRS-GA performs better than two baselines in terms of battery life consumption, as shown in Fig. 12(a). With the increase of generations, the battery life consumption of RRS-GA presents a gradual decline trend, which indicates that gene mutation and crossover constantly generate excellent solutions for RRS-GA. When the number of individuals is 20 and the number of population iterations is 25, RRS-GA reduces battery life consumption by 15.17% compared with RRS-MRN, and reduces battery life consumption by 17.87% compared with RRS-MBL. Figures 12(b) and (c) present the performance of RRS-GA in terms of average numbers of regeneration nodes and LISLs occupied in lightpaths. RRS-GA uses more regeneration nodes than RRS-MRN, which means that RRS-GA reduces battery life consumption by using more relay satellites with low battery DOD for lightpath regeneration. Compared with RRS-MRN and RRS-MBL, RRS-GA has a slight increase in the LISLs occupied in lightpaths, because some lightpaths occupying more LISLs may pass through satellites having the battery at a shallow DOD. Instead of reducing the total energy consumption of lightpath regeneration, EE-RR is to reduce the energy consumption of batteries at the deep DOD. When there are batteries with deep DOD at the satellites in the shortest path, RRS-GA may try to avoid using those satellites, and choose a longer path to establish the lightpath to reduce battery life consumption, which will increase the number of regeneration nodes and LISLs occupied by the lightpath.

Fig. 12. Performance comparison of RRS-GA under different numbers of individuals and generations, (a) battery life consumption, (b) number of regeneration nodes, (c) number of occupied LISLs.

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Table 5. Simulation results of two baselines

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Earlier, we have analyzed the performances of different EE-RR schemes under the slight network load (no request blocking). Next, we compare different schemes under moderate and heavy network loads (both having request blocking). The numbers of requests per snapshot are 800 and 1000 under moderate and heavy network load, respectively. Figure 13 illustrates the performance comparison between two baselines and RRS-GA under moderate and heavy network loads. Due to that regeneration nodes can convert the wavelength of the lightpath, RRS-MBL has the most flexibility of the wavelength assignment in lightpaths. Therefore, RRS-MBL using SP has the smallest probability of request blocking, as shown in Fig. 13(d). RRS-GA may try to choose a longer path to establish the lightpath to reduce battery life consumption when there are batteries with deep DOD at the satellites in the shortest path. Considering more LISLs may be used in lightpaths to facilitate satellites having the battery at a shallow DOD for lightpath regeneration, RRS-GA occupies more idle wavelengths to establish lightpaths and inevitably leads to an increase in the probability of request blocking. Under the moderate network load, the increase in the probability of request blocking of RRS-GA is insignificant, because RRS-GA uses more regeneration nodes in lightpaths than RRS-MRN, enabling more flexible wavelength assignment to alleviate request blocking. However, under the heavy network load, the lack of wavelength resources has the more serious influence on request blocking. How to make a trade-off between request blocking and battery life consumption under the heavy network load is our further research content for EE-RR.

Fig. 13. Performance comparison under moderate and heavy network loads, (a) battery life consumption, (b) number of regeneration nodes, (c) number of occupied LISLs, (d) probability of request blocking.

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5. Discussion and conclusion

5.1 Discussion

This paper sets the bandwidth granularity of traffic requests as one wavelength, and the small-granularity traffic is added and dropped at the source and destination satellites. In fact, the satellite-ground access and traffic grooming are also important for the energy efficiency of lightpaths, which will be covered in our subsequent researches. Moreover, this paper uses the BER evolution model for the repeated optical links to approximate the deterioration of QoT in lightpaths of the worst case. and only the noise accumulation from ASE and DS crosstalk is considered. The power penalty of main signals is assumed to be compensated at the receivers of regeneration nodes. In addition, this paper doesn’t specifically design the wavelength assignment for EE-RR, and only the traditional FF algorithm is used. The regeneration nodes can readjust the wavelength occupied by lightpaths, and how to improve energy efficiency while flexibly adjusting wavelength assignment is our further research focus.

5.2 Conclusion

This paper proposes EE-RR to reduce the battery life consumption of lightpath regeneration in SONs under the translucent optical payload architecture. The MBH is defined based on the BER evolution model for the repeated optical links, which can approximate the deterioration of QoT in lightpaths, facilitating designating the regeneration nodes of lightpaths in SONs under different LISL configuration parameters. Two greedy baselines RRS-MRN and RRS-MBL are proposed for EE-RR of lightpaths. Considering that greedy baselines cannot achieve the ideal global optimization in the large-scale solution domain, we develop RRS-GA to improve the optimization ability of EE-RR in SONs. The numerical simulation shows that blindly reducing regeneration nodes in lightpaths cannot reduce overall battery life consumption of lightpath regeneration. Under the slight network load without request blocking, RRS-GA uses more generation nodes for lightpath regeneration, but reduces battery life consumption by 15.17% compared with RRS-MRN, and reduces battery life consumption by 17.87% compared with RRS-MBL.

Funding

National Natural Science Foundation of China (62125103, 62171050); Fundamental Research Funds for Central Universities (2023PY08); State Key Laboratory of Information Photonics and Optical Communications (IPOC2021ZT15); Fund of Key Laboratory of Computer System and Architecture (CARCH201906); BUPT Excellent Ph.D. Students Foundation (CX2023232).

Acknowledgment

We thank the National Natural Science Foundation of China (62125103, 62171050), the Fund of Key Laboratory of Computer System and Architecture (CARCH201906), the State Key Laboratory of Information Photonics and Optical Communications (IPOC2021ZT15), the Fundamental Research Funds for Central Universities (2023PY08), the BUPT Excellent Ph.D. Students Foundation (CX2023232) for supporting this work.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Notations	Explanation
V	Satellite nodes in the SON
E	LISLs in the SON
W	Number of wavelengths in LISLs
G(V,E)	SON topology
EV	Satellites in eclipse
r(s,d)	Request in the SON, s is source satellite, and d is destination satellite
D_v	Battery DOD of satellite v∈V
P_r	Lightpath of request r, P_r={RL_r, RN_r}
RN_r	Regeneration nodes designated in lightpath P_r
RL_r	LISLs used in lightpath P_r

Parameter	Value
Orbit inclination	53°
Orbit altitude	550Km
Phase factor	1
Number of LISLs per satellite	4
Maximum output power of solar panels	10000 Watt
Snapshot duration	10 Minute
Battery capacity C_max	40000 Watt*Minute
Power consumption P_SC	1 Watt
Power consumption P_BF	40 Watt
Power consumption P_RF	20 Watt
Power consumption P_LISL	20 Watt per LISL
Constant parameter ξ	1 Watt/Gbps
Constant parameter ɛ	1.4
Bit rate per wavelength	10 Gbps

Baseline	MRN, SP	MBL, SP	MRN, KSP	MBL, KSP
Battery life consumption	57.54	63.93	49.41	51.03
Number of regeneration nodes	7.72	8.63	7.71	8.46
Number of occupied LISLs	31.62	31.62	31.64	31.65

Notations	Explanation
V	Satellite nodes in the SON
E	LISLs in the SON
W	Number of wavelengths in LISLs
G(V,E)	SON topology
EV	Satellites in eclipse
r(s,d)	Request in the SON, s is source satellite, and d is destination satellite
D_v	Battery DOD of satellite v∈V
P_r	Lightpath of request r, P_r={RL_r, RN_r}
RN_r	Regeneration nodes designated in lightpath P_r
RL_r	LISLs used in lightpath P_r

Parameter	Value
Orbit inclination	53°
Orbit altitude	550Km
Phase factor	1
Number of LISLs per satellite	4
Maximum output power of solar panels	10000 Watt
Snapshot duration	10 Minute
Battery capacity C_max	40000 Watt*Minute
Power consumption P_SC	1 Watt
Power consumption P_BF	40 Watt
Power consumption P_RF	20 Watt
Power consumption P_LISL	20 Watt per LISL
Constant parameter ξ	1 Watt/Gbps
Constant parameter ɛ	1.4
Bit rate per wavelength	10 Gbps

Energy-efficient regeneration routing in satellite optical networks under translucent optical payload architectures

Abstract

1. Introduction

2. Theoretical model of SONs

2.1 Networking components

2.2 Translucent optical payload architecture

2.3 MBH of regeneration routing

2.4 Energy consumption analysis

2.5 Energy support of satellites

3. Design of EE-RR

3.1 Baseline RRS-MRN

3.2 Baseline RRS-MBL

3.3 RRS-GA

3.4 Time complexity analysis

4. Performance evaluation

4.1 Numerical analysis related to MBH

4.2 Performance evaluation of regeneration routing

5. Discussion and conclusion

5.1 Discussion

5.2 Conclusion

Funding

Acknowledgment

Disclosures

Data availability

References

Data availability

Cited By

Figures (13)

Tables (10)

Equations (19)

Optics Express

Acronym	Full name
TON	Terrestrial optical network
LEO	Low-earth orbit
FSO	Free space optical
RF	Radio frequency
LISL	Laser inter-satellite link
SON	Satellite optical network
DOD	Depth of discharge
WDM	Wavelength division multiplexing
SNR	Signal-to-noise ratio
BER	Bit error rate
FEC	Forward error correction
EDFA	Erbium-doped fiber amplifier
ASE	Amplifier spontaneous emission
DS	Doppler shift
QoT	Quality of transmission
OEO	Optical-electrical-optical
DSP	Digital signal processing
EE-RR	Energy-efficient regeneration routing
MBH	Maximum bypass hops
RRS-MRN	Regeneration routing scheme minimizing the number of regeneration nodes
RRS-MBL	Regeneration routing scheme minimizing single satellite’s battery life consumption
RRS-GA	Regeneration routing scheme using genetic algorithms
HydRON	High thRoughput Optical Network
ESA	European space agency
OXC	Optical cross connect
3R	Re-amplifying, re-shaping, and re-timing